They find that vinyl triflates and cyclic vinyl triflates will react with [Ph3C]+[HCB11Cl11]– and triethylsilane to generate vinyl cations that can then be trapped through a C-H insertion reaction. For example, cyclohexenyl triflate 1 reacts in a cyclohexane solvent to give the insertion product 2.

The reactions of isomers 3 and 4 give different ratios of the two products 5 and 6. In both cases, the cyclohexyl is trapped predominantly at the site of the triflate substituent. This means that the mechanism cannot involve a cyclohexene intermediate, since then the two ratios should be identical.

They performed molecular dynamic trajectory analysis at the M062X/6-311+G(d,p) level, starting with the two transition states leading from 3 (TS3) and 4 (TS4), the only transition states located for the insertion reaction. The structures of these TSs are shown in Figure 1.

TS3

TS4

Figure 1. M062X/6-311+G(d,p) optimized geometries of TS3 and TS4.

The trajectories end up in two product basins associated with 5 and 6 starting with either TS3 or TS4. Thus, these transition states are ambimodal, and typical of reactions where dynamic effects dominate. For the reaction of 3, the majority of the trajectories starting at TS3 end up as 5, consistent with the experiments. Similarly, for the trajectories that start at TS4, the majority end up as 6, consistent with experiments.

Once again, we see that relatively simple organic reactions do not follow simple reaction mechanisms, that a single transition state leads to two different products and the product distributions are dependent on reaction dynamics. This may not be too surprising for the vinyl cation insertions given the many examples provide by the Tantillo group of cation rearrangements that are controlled by reaction dynamics (see for examples, this post and this post).

Sarpong and Tantillo have examined the acid-catalyzed Prins/semipinacol rearrangement of hydroxylated pinenes, such as Reaction 1.1

Rxn 1

Interestingly, only the fenchone scaffold products, like 1, are observed and the camphor scaffold products, like 2, are not observed. Cation intermediates are likely, and this means that a primary alkyl shift is taking place in preference to a tertiary alkyl shift, see Scheme 1.

Scheme 1.

Primary alkyl shift

Tertiary alkyl shift

They proposed the following key steps in the reaction mechanism:

ωB97X-D/6-31+G(d,p) computations find a flat surface around cation intermediate 4: the TS leading to 5 and 6 are only 1.3 and 3.3 kcal mol-1, respectively. Since these small barriers are quite susceptible to changes in basis set and functional, and since Tantillo has found many examples of post-transition state bifurcations in cation systems, the authors reasonably decided to conduct molecular dynamics trajectories originating at the TS connecting 3 and 4. The geometries of the critical points are shown in Figure 1.

The trajectory study shows all the usual characteristics of reactions that are under dynamic control. A third of the trajectories show recrossing of the barrier, typical of very flat surfaces. Nearly all of the remaining trajectories led to 5, with only 2 trajectories (~1%) leading to 6. The dynamics are understandable in terms of favoring the primary alkyl shift over the tertiary since a significantly smaller mass needs to move in the former case.

At the recent ACS meeting in New Orleans, Ken Houk spoke at the Dreyfus award session in honor of Michele Parrinello. Ken’s talk included discussion of some recent molecular dynamics studies of pericyclic reactions. Because of their similarities in approaches and observations, I will discuss three recent papers from his group (which Ken discussed in New Orleans) in this post.

The Cope rearrangement, a fundamental organic reaction, has been studied extensively by computational means (see Chapter 4.2 of my book). Mackey, Yang, and Houk examine the degenerate Cope rearrangement of 1,5-hexadiene with molecular dynamics at the (U)B3LYP/6-31G(d) level.1 They examined 230 trajectories, and find that of the 95% of them that are reactive, 94% are trajectories that directly cross through the transition zone. By this, Houk means that the time gap between the breaking and forming C-C bonds is less than 60 fs, the time for one C-C bond vibration. The average time in the transition zone is 35 fs. This can be thought of as “dynamically concerted”. For the other few trajectories, a transient diradical with lifetime of about 100 fs is found.

The dimerization of cyclopentadiene finds the two [4+2] pathways merging into a single bispericylic transition state. 2 Only a small minority (13%) of the trajectories sample the region about the Cope rearrangement that interconverts the two mirror image dimers. These trajectories average about 60 fs in this space, which comes from the time separation between the formation of the two new C-C bonds. The majority of the trajectories quickly pass through the dimerization transition zone in about 18 fs, and avoid the Cope TS region entirely. These paths can be thought of as “dynamically concerted”, while the other set of trajectories are “dynamically stepwise”. It should be noted however that the value of S2 in the Cope transition zone are zero and so no radicals are being formed.

Finally, Yang, Dong, Yu, Yu, Li, Jamieson, and Houk examined 15 different reactions that involve ambimodal (i.e. bispericyclic) transition states.3 They find a strong correlation between the differences in the bond lengths of the two possible new bond vs. their product distribution. So for example, in the reaction shown in Scheme 1, bond a is the one farthest along to forming. Bond b is slightly shorter than bond c. Which of these two is formed next is dependent on the dynamics, and it turns out the Pab is formed from 73% of the trajectories while Pac is formed only 23% of the time. This trend is seen across the 15 reaction, namely the shorter of bond b or c in the transition state leads to the larger product formation. When competing reactions involve bonds with differing elements, then a correlation can be found with bond order instead of with bond length.

Bispericyclic transition states arise when two pericyclic reactions merge to a common transition state. This leads to a potential energy surface with a bifurcation such that reactions that traverse this type of transition state will head towards two different products. The classic example is the dimerization of cyclopentadiene, involving two [4+2] Diels-Alder reactions. Unusual PESs are discussed in my book and in past blog posts.

Houk and coworkers have now identified a bispericyclic transition state involving two [6+4] cycloadditions.1 Reaching back to work Houk pursued as a graduate student with Woodward for inspiration, these authors examined the reaction of tropone 1 with dimethylfulvene 2. Each moiety can act as the diene or triene component of a [6+4] allowed cycloaddition:

The product with fulvene 2 as the 6 π-e component and tropone as the 4 π-e component [6F+4T] is 3, while reversing their participation in the [6T+4F] cycloaddition leads to 4. A variety of [4+2] reactions are also possible. All of these reactions were investigated at PCM/M06-2X/6-311+G(d,p)//B3LYP-D3/6-31G(d). The reaction leading to 3 is exothermic by 3.0 kcal mol-1, while the reaction to 4 endothermic by 1.3 kcal mol-1.

Interestingly, there is only one transition state that leads to both 3 and 4, the first known bispericyclic transition state for two conjoined [6+4] cycloadditions. The barrier is 27.9 kcal mol-1. The structures of the two products and the transition state leading to them are shown in Figure 1. 3 and 4 can interconvert through a Cope transition state, also shown in Figure 1, with a barrier of 26.3 kcal mol-1 (for 4 → 3).

3

4

TS [6+4]

TS Cope

Figure 1. B3LYP-D3/6-31G(d) optimized geometries.

Given that a single transition leads to two products, the product distribution is dependent on the molecular dynamics. A molecular dynamics simulation at B3LYP-D3/6-31G(d) with 117 trajectories indicates that 4 is formed 91% while 3 is formed only 9%. Once again, we are faced with the reality of much more complex reaction mechanisms/processes than simple models would suggest.

A few nice review/opinion pieces have been piling up in my folder of papers of interest for this Blog. So, this post provides a short summary of a number of review articles that computationally-oriented chemists may find of interest.

Holy Grails in computational chemistry

Houk and Liu present a short list of “Holy Grails” in computationally chemistry.1 They begin by pointing out a few technical innovations that must occur for the Grails to be found: development of a universal density functional; an accurate, generic force field; improved sampling for MD; and dealing with the combinatorial explosion with regards to conformations and configurations. Their list of Grails includes predicting crystal structures and structure of amorphous materials, catalyst design, reaction design, and device design. These Grails overlap with the challenges I laid out in my similarly-themed article in 2014.2

Post-transition state bifurcations and dynamics

Hare and Tantillo review the current understanding of post-transition state bifurcations (PTSB).3 This type of potential energy surface has been the subject of much of Chapter 8 of my book and many of my blog posts. What is becoming clear is the possibility of a transition state followed by a valley-ridge inflection leads to reaction dynamics where trajectories cross a single transition state but lead to two different products. This new review updates the state-of-the-art from Houk’s review4 of 2008 (see this post). Mentioned are a number of studies that I have included in this Blog, along with reactions involving metals, and biochemical systems (many of these examples come from the Tantillo lab). They close with the hope that their review might “inspire future studies aimed at controlling selectivity for reactions with PTSBs” (italics theirs). I might offer that controlling selectivity in these types of dynamical systems is another chemical Grail!

The Hase group has a long review of direct dynamics simulations.5 They describe a number of important dynamics studies that provide important new insight to reaction mechanism, such as bimolecular SN2 reactions (including the roundabout mechanism) and unimolecular dissociation. They write a long section on post-transition state bifurcations, and other dynamic effects that cannot be interpreted using transition state theory or RRKM. This section is a nice complement to the Tantillo review.

Benchmarking quantum chemical methods

Mata and Suhm look at our process of benchmarking computational methods.6 They point out the growing use of high-level quantum computations as the reference for benchmarking new methods, often with no mention of any comparison to experiment. In defense of theoreticians, they do note the paucity of useful experimental data that may exist for making suitable comparisons. They detail a long list of better practices that both experimentalists and theoreticians can take to bolster both efforts, leading to stronger computational tools that are more robust at helping to understand and discriminate difficult experimental findings.

Bispericyclic reactions occur when two different pericyclic reactions merge to have a single transition state. An example of this is the joining of two [3,3]-sigmatopic rearrangements of 1 that merge to have a single transition state. Lopez, Faza, and Lopez have examined the dynamics of this reaction.1

Because of the symmetry of the species along this reaction pathway, the products of the two different rearrangements are identical, and will be formed in equal amounts, though they are produced from a single transition state with the reaction pathway bifurcating due to a valley-ridge inflection post TS.

The interesting twist that is explored here is when 1 is substituted in order to break the symmetry. The authors have examined 3x with either fluorine, chlorine, or bromine. The critical points on the reactions surface were optimized at M06-2X/Def2TZVPP. In all three cases a single bispericyclic transition state 3TS1x is found, which leads to products 4a and 4b. A second transition state 4TSx corresponds to the [3,3]-rearrangement that interconverts the two products. The structures of 1TS, 3TS1F, and 3TS1Cl are shown in Figure 1.

The halogen substitution breaks the symmetry of the reaction path. This leads to a number of important changes. First, the C4-C5 and C7-C8 distances, which are identical in 1TS, are different in the halogen cases. Interestingly, the distortions are dependent on the halogen: in 3TS1F C4-C5 is 0.2 Å longer than C7-C8, but in 3TS1Cl C7-C8 is much longer (by 0.65 Å) than C4-C5. Second, the products are no longer equivalent with the halogen substitution. Again, this is halogen dependent: 4bF is 4.0 kcal mol-1 lower in energy than 4aF, while 4aCl is 8.2 kcal mol-1 lower than 4bCl.

These difference manifest in very different reaction dynamics. With trajectories initiated at the first (bispericyclic) transiting state, 89% end at 4bF and 9% end at 4aF, a ratio far from unity that might be expected from both products resulting from passage through the same TS. The situation is even more extreme for the chlorine case, where all 200 trajectories end in 4aCl. This is yet another example of the role that dynamics play in reaction outcomes (see these many previous posts).

Enzyme SpnF is implicated in catalyzing the putative [4+2] cycloaddition taking 1 into 3. Houk, Singleton and co-workers have now examined the mechanism of this transformation in aqueous solution but without the enzyme.1 As might be expected, this mechanism is not straightforward.

Reactant 1, transition states, and products 2 and 3 were optimized at SMD(H2O)/M06-2X/def2-TZVPP//B3LYP-D3(BJ)//6-31+G(d,p). Geometries and relative energies are shown in Figure 1. The reaction 1 → 2 is a formal [6+4] cycloaddition, and the reaction 1 → 3 is a formal [4+2] cycloaddition. Interestingly, only a single transition state could be located TS1. It is a bispericyclic TS (see Chapter 4 of my book), where these two pericyclic reaction sort of merge together. After TS1 is traversed the potential energy surface bifurcates, leading to 2 or 3. This is yet again an example of a single TS leading to two different products. (See the many posts I have written on this topic.) The barrier height is 27.6 kcal mol-1, with 2 lying 13.1 kcal mol-1 above 3. However, the steepest descent pathway from TS1 leads to 2. There is a second transition state TScope that describes a Cope rearrangement between 2 and 3. Using the more traditional TS theory description, 1 undergoes a [6+4] cycloaddition to form 2 which then crosses a lower barrier (TScope) to form the thermodynamically favored 3, which is the product observed in the enzymatically catalyzed reaction.

Molecular dynamics computations were performed on this system by tracking trajectories starting in the neighborhood of TS1 on a B3LYP-D2/6-31G(d) PES. The results are that 63% of the trajectories end at 2, 25% end at 3, and 12% recross back to reactant 1, suggesting an initial formation ratio for 2:3 of 2.5:1. The reactions are very slow to cross through the “transition zone”, typically 2-3 times longer than for a usual Diels-Alder reaction (see this post).

Once again, we see an example of dynamic effects dictating a reaction mechanism. The authors pose a tantalizing question: Can an enzyme control the outcome of an ambimodal reaction by altering the energy surface such that the steepest downhill path from the transition state leads to the “desired” product(s)? The answer to this question awaits further study.

Houk and Doubleday report yet another example of dynamic effects in reactions that appear to be simple, ordinary organic reactions.1 Here they look at the Diels-Alder reaction of tetrazine 1 with cyclopropene 2. The reaction proceeds by first crossing the Diels-Alder transition state 3 to form the intermediate 4. This intermediate can then lose the anti or syn N2, through 5a or 5s, to form the product 6. The structures and relative energies, computed at M06-2X/6-31G(d), of these species are shown in Figure 1.

317.4

4-33.2

5a-28.9

5s-20.0

6-86.2

Figure 1. M06-2X/6-31G(d) optimized geometries and energies (relative to 1 + 2) of the critical points along the reaction of tetrazine with cyclopropene.

The large difference in the activation barriers between crossing 5a and 5s (nearly 9 kcal mol-1) suggests, by transition state theory, a preference of more than a million for loss of the anti N2 over the syn N2. However, quasiclassical trajectory studies, using B3LYP/6-31G(d), finds a different situation. The anti pathway is preferred, but only by a 4:1 ratio! This dynamic effect arises from a coupling of the v3 mode which involves a rocking of the cyclopropane ring that brings a proton near the syn N2 functionality, promoting its ejection. In addition, the trajectory studies find short residence times within the intermediate neighborhood for the trajectories that lead to the anti product and longer residence times for the trajectories that lead to the syn product. All together, a very nice example of dynamic effects playing a significant role in a seemingly straightforward organic reaction.

Schmittel has examined the thermolysis of 1, which undergoes a Garratt-Braverman rearrangement followed by a [1,5]-H migration to produce 3.1 The product 3 is formed in a 10.3:1 ratio of E to Z consistently over the temperature range of 60 – 140 °C. This non-changing ratio is unusual. The difference in the computed (UB3LYP/6-31g(d)) free energy of activation for the step 2 → 3 ranges from 2.35 to 2.56 kcal mol-1 for this temperature range, manifesting in a predicted E:Z ratio of 24.9 at 60 °C to 22.7 at 140 °C.

The computed structures of 1-3 along with the transition states are shown in Figure 1. The activation free energy for the first step (Garrat-Braverman) is 30.9 kcal mol-1. This is about 30 kcal mol-1 larger than the barrier for the second step. Schmittel suggests that a non-statistical effect is manifesting here. The molecule crosses the first TS and then follows a downhill path directly over TS2E without spending any time in the region of the intermediate 2. A few computed trajectories all indicate that it takes less than 50 fs from the time the reaction crosses TS1 until the hydrogen migrates, supporting the notion that vibrational relaxation within the intermediate 2 is not occurring. This reaction is yet another example of dynamic effects dictating product distributions.

1a0.0

1b12.3

TS130.9

2-14.6

TS2E0.5

TS2Z2.8

3E-50.5

3Z-46.1

Figure 1. UB3LYP/6-31G(d) optimized structures and relative free energies (kcal mol-1) for the reaction 1 → 3. (Note that a conformational change must first take 1a into 1b before the reaction can take place.)

The di-π-methane photorearrangement has been known for many years, first studied by Zimmerman.1,2 The triplet photorearrangement gives an interesting rearranged product; and the mechanism of this photorearrangement of 1 into 2 has now been examined by the Houk group using computational techniques, including trajectory analysis. The proposed mechanism is that excitation to the triplet state 1* is followed by rearrangement to the triplet intermediate INT1* which then rearranges to the triplet INT2*. Intersystem crossing then leads to the singlet product 2.

The PES for this rearrangement was explored3 at CASMP2(10,10)/6-31G(d)//CASSCF(10,10)/6-31G(d), with geometries and relative energies shown in Figure 1, as well as at (U)M06-2x/6-31G(d) and (U)B3LYP/6-31G(d); they all give qualitatively the same result. The first TS is the rate limiting step, and the second TS lies only 1-2 kcal mol-1 above the intermediate INT1. So, the reaction appears to be two steps, but with such a low barrier for the second step, dynamic effects might be important as trajectories might cross INT1* and go over TS2* without residing in the intermediate well for any appreciable time – a seemingly one step reaction. Note than no TS for directly traversing from 1* to INT2* was found.

Now in a follow-up study, Houk and co-workers4 performed trajectories analysis on the M06-2x/6-31G(d) PES. A total of 256 trajectories were initiated at TS1* and 241 ended at INT2* within 1500fs. Of these, 24 trajectories resided for less than 60fs within the region of INT1, a time less than a C-C vibration. Furthermore, the lifetime of INT1 that is predicted by RRKM is much longer (about 500fs) than what is observed in the trajectories (about 200 fs). Thus, there is significant dynamic effects in this excited state rearrangement, though INT1 is always sampled.